The flowmeter, as an essential part of the anesthesia machine, may be adjusted by a doctor to provide for a suitable flow of oxygen to a patient. The existing flowmeter for the anesthesia machine has the following problems that: (1) the flowmeter float beats during the normal operation of the bellows of the anesthesia machine; (2) the air within the flowmeter cannot be discharged effectively in the case of excessive air resistance at the flowmeter outlet; and (3) its structure is complex and its manufacture cost is high.